I posted this response in LTU, but it bears repeating. Orthogonality (or representational independence), not size, is the relevant criteria. Harmonic analysis

I posted this response in LTU, but it bears repeating. Orthogonality (or representational independence), not size, is the relevant criteria. Harmonic analysis is the appropriate comparison. While every complete basis can represent any function in the relevant function space, it is better at representing some than others; notably the functions which are a finite linear combination of the basis functions. So trigonometric series represent one kind of function very efficiently, wavelets another. It's similar with programming languages. Of course the orthogonal core may be mostly of interest to the language implementer,as orthogonality should, in the most faithful sense of the word, make the implementation of one construct independent of implementing another construct, particularly in optimization.